High‐Dimensional Oaxaca–Blinder Decomposition With an Application to Gender and Hukou Discrimination in the Chinese Labour Market

High‐dimensional covariates can help justify the unconfoundedness assumption in causal inference and reduce concerns about model misspecification. This paper explores the estimation and inference of counterfactual cumulative distribution functions (CDFs) in a high‐dimensional setting, with a focus on the distributional Oaxaca–Blinder decomposition. We propose two semi‐parametric estimators for the counterfactual CDF, deriving their asymptotic properties and demonstrating that both estimators are semiparametrically efficient, even when using finite‐dimensional controls. We apply the proposed methods to examine gender and hukou‐related wage discrimination in the Chinese labour market. Our findings reveal significant gender wage discrimination, but no evidence of hukou‐based wage discrimination, in contrast to results obtained using the traditional linear Oaxaca–Blinder decomposition with finite‐dimensional covariates.